This gear ratio calculator works out the ratio, output speed, and torque change of a gear or pulley pair from the number of teeth (or diameters). It is the quick reference for anyone building a geared mechanism, a lathe drive, a clock, or a model where input and output speeds must match.
Ratio, speed and torque
The gear ratio is the driven (output) teeth divided by the driving (input) teeth. A ratio greater than one gears down — the output turns slower but with more torque; less than one gears up — faster but with less torque. Speed and torque trade off inversely: gearing down by 3:1 cuts the output speed to a third and (ignoring losses) roughly triples the torque. The calculator returns all three so you can size a drive to the job.
For belts and pulleys the same maths uses pulley diameters instead of teeth. In a gear train with several stages, the overall ratio is the product of the individual stage ratios, which is how small gears combine to give large reductions.
Designing a drive
Start from what the output must do — a target speed or a required torque — and work back to the ratio, then choose gear sizes that achieve it with teeth counts that mesh and fit the space. Remember real drives lose some power to friction, so size in a margin rather than assuming perfect torque multiplication.
A 12-tooth pinion drives a 36-tooth gear; the motor runs at 1500 RPM.
- Ratio = driven ÷ driving = 36 ÷ 12 = 3:1 (a 3:1 reduction).
- Output speed = 1500 ÷ 3 = 500 RPM.
- Output torque ≈ 3 × input torque (minus friction losses).
A 3:1 reduction gives 500 RPM at the output with about three times the input torque.
